Ann Widdecombe's murder is alleged to have been "politically and ideologically motivated", a court has heard.
Joshua Kerry, 28, is accused of driving 265 miles to the Devon home of Reform UK spokeswoman and former Tory minister Widdecombe on 8 July before hitting her in the head 21 times with a hammer.
She died aged 78 and Kerry was charged with her murder on 20 July.
He was last week charged with a further offence of preparing an act of terrorism between 31 May 2024 and 8 July 2026, involving Nigel Farage.
Prosecutors say the murder and terrorism charges represent "a single course of conduct and are inextricably linked".
Kerry appeared at the Old Bailey by prison video-link from Belmarsh prison, in south London, on Friday afternoon, where the two charges were officially joined.
He is accused of researching "targets" and travelling to the home of the Reform UK leader, attempting to gain entry.
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Westminster Magistrates' Court heard on Tuesday Mr Farage's partner returned home to discover damage to the main front door on Sunday 20 April last year.
Part of the wooden door frame was hanging off and there was a bottle of lighter fluid in the porch, the court was told.
Prosecutors also allege Kerry researched "politicians and other prominent figures" between 31 May 2024 and 8 July 2026, including identifying the home addresses of Ms Widdecombe and Mr Farage.
Wearing glasses and a grey, prison-issue tracksuit, he sat with his arms folded and legs crossed.
Kerry, from Rotherham, South Yorkshire, was remanded in custody ahead of his trial on 8 June next year and will next appear in court in January.
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